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Abstract
Let C be a k-gonal curve with a simple pencil |F| of degree k. First we show that if C has a complete for
, then
= |
| + B for some
, where B is the base locus of
. Using this, |
| =
and K(−
) is very ample for any
if
. Also we prove that K(−
) is normally generated if
is simple and
(respectively
) for k ≥ 7 (respectively 4 ≤ k ≤ 6).
Acknowledgment
This work was supported by grant No. R04-2001-000-00167-0 from the Korea Science and Engineering Foundation for both authors.
This work was supported by grant No. R14-2002-007-01000-1, R01-2002-000-00051-0 from the Korea Science and Engineering Foundation for second author.
Notes
#Communicated by S. Kleiman.